The major factors determining drug responses are the input and disposition rates controlling pharmacokinetics, drug distribution to the site of action (biophase), the mechanism of drug action in altering mediator or receptor levels, and turnover and transduction processes. A major advance in quantitating pharmacologic responses came from our recognition that diverse pharmacodynamic effects can be characterized using a family of four basic (and extended) indirect response models. These (and most) models require analysis using differential equations which usually cannot be fully solved analytically. This project seeks to characterize and quantify the general properties of drugs acting on turnover processes which are important for numerous body functions, structures, or biomarkers. Our specific aims include continued development of extended indirect models for responses generated from a precursor pool as relevant for most hormones and endogenous substances, explore multi-pool lifespan based indirect response models accounting for variability of lifespans of most cells derived from the hematopoietic system, develop advanced models for drugs with target-mediated disposition accounting for several possible control factors and turnover of reactive sites as relevant for a growing array of biotechnology products, and extend indirect response models to handle several types of drug-drug interactions which describe natural synergy and apply to many joint effects of drugs such as immunosuppressants and chemotherapeutic agents. Advanced methods of calculus and simulations will be employed to seek exact or approximate solutions or behaviors for these models, to identify how the onset, extent, return, duration, integrals of response, and steady-state of responses are controlled, to recover parameters more easily from experimental data, and to discriminate among diverse models available to describe typical data. This research addresses the considerable need in drug development for better strategies for utilizing biomarkers and for quantitating and predicting drug effects. These efforts will yield improved insights and methods for understanding and characterizing the time-course of drug responses as related to major mechanisms of physiology and pharmacologic action.